WS MoreOrLess: The maths of dating

Summary

More or Less: The Maths of Dating

BBC Radio 4 – February 2, 2015
Host: Tim Harford
Guests: Matt Parker (Mathematician, Comedian, Author), Professor Jason Gardosi (Perinatal Institute, UK), Listeners Penelope Chaney & Eleanor Marshall

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Episode Overview

In this episode, Tim Harford explores the role of mathematics in life’s big decisions, focusing on two topics: the maths of finding the perfect life partner (the “optimal stopping problem”) and the statistical reality of pregnancy due dates. Featuring insights from mathematician and comedian Matt Parker and perinatal expert Professor Jason Gardosi, the episode delves into the practical applications and limitations of mathematical modeling in everyday life.

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Key Discussion Points & Insights

1. The Maths of Dating – The Optimal Stopping Problem

• Introduction to the Problem (00:19–01:11):
  Tim Harford consults Matt Parker about whether math can help one find the right life partner.

  • Matt humorously reflects:
    “I'm pleased to say I'm happily married, but occasionally I have doubts as to whether maybe I settled down too soon. Could I have done better if I waited?” (00:55 – Matt Parker)

• Explanation of the Model (01:11–02:53):
  Matt Parker and Tim’s guest mathematician discuss the “optimal stopping problem”—when to stop searching and make a choice.

  • The scenario: You can’t revisit rejected partners, but if you settle too soon you might miss out on better options.
  • The math: Estimate how many people you’ll date in your life; take the square root of that number (e.g., √100 = 10 for 100 possible dates). Interview and automatically reject the first 10, keeping notes. Then, pick the next person who matches or exceeds the best from the first sample.
    • “If you want to get the best person on average, you ... calculate the square root of that number of people. ... Once you've gone through that, you then keep dating people until you meet someone who is as good as or better than anyone you saw in your original sample.” (01:45 – Mathematician/Expert)

• Limitations of the Model (02:53–03:35):
  Matt Parker cautions about real-life applicability.

  • “There are all sorts of assumptions that we're making … what counts as an interview … how long do you need to date … we're assuming … quality doesn’t change … you know with certainty how many people you could possibly date.” (02:53 – Matt Parker)
  • His guest agrees: “A mathematical model is only as good as the starting assumptions … I wouldn’t recommend living life following this down to the algorithm ...” (03:35 – Mathematician/Expert)
  • Key takeaway: People, on average, settle down too soon.

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2. The Maths of Pregnancy Due Dates

• Listener Question Introduction (04:03–05:39):
  Inspired by the idea of finding “the one,” listener Penelope Chaney and friend Eleanor Marshall both expect their babies on the same day—April 4.

  • They wonder: What is the probability both children actually share the same birthday?
  • Tim brings in Professor Jason Gardosi for expert perspective.

• Methods for Calculating Due Dates (05:39–06:01):

  • The classic method: Add 280 days to the first day of the last menstrual period.
    • “That is old school ... still being practiced in many countries ... the first day of the last menstrual period from which to count the length of pregnancy.” (05:39 – Prof. Gardosi)
  • Today’s approach: Ultrasound measurement is more accurate.

• Chances of Being Born on Due Date (06:01–07:03):

  • Only 4.4% of babies are born on their estimated date, even in normal, low-risk pregnancies (UK data).
    • "Most babies are not born on the predicted or estimated date of delivery, but in fact only about 4%." (06:30 – Prof. Gardosi)
    • The probability of both Penelope and Eleanor delivering on April 4: roughly 1 in 500.

• Reactions from Listeners (07:03–07:20):

  • Eleanor: “It’s a wonderful coincidence, but it’s not like we did it on purpose ... that would be weird. We’re not that close friends.”

• Why Set a Due Date at All? (07:20–08:27):

  • The due date is a useful benchmark for doctors, not an absolute to expect.
    • “Medical professionals use [the due date] as a benchmark to let them evaluate test results and judge how the baby's developing.” (07:20 – Tim Harford)
  • 94% of babies are born within two weeks of the estimated date.
  • For two normal pregnancies with the same estimated date, the chance both babies actually share a birthday (allowing for early or late arrival): about 1 in 30.
    • “It’s one in 30.” (08:20 – Tim Harford)
    • “That is quite high.” (08:29 – Eleanor Marshall)

• Key Takeaway for Expectant Mothers (08:38–End):

  • The concept of a “due date” is somewhat arbitrary; don’t stress about overdue babies.
    • “You shouldn't expect a baby to pay attention to what is, after all, a fairly arbitrary metric.” (08:38 – Tim Harford paraphrasing Prof. Gardosi)

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Notable Quotes & Memorable Moments

• Maths and Love:
  “If you want to get the best person on average, you ... calculate the square root of that number of people.”
  — Mathematician/Expert, 01:45

• Real World vs. Model:
  “A mathematical model is only as good as the starting assumptions … I wouldn’t recommend living life following this down to the algorithm ...”
  — Mathematician/Expert, 03:35

• Due Dates are Rarely Right:
  “Only about 4% ... actually born on the predicted or estimated date.”
  — Prof. Jason Gardosi, 06:30

• Great Odds for Coincidences:
  “It’s one in 30.”
  — Tim Harford, on two unrelated babies with the same estimated delivery date sharing a birthday, 08:20

• On Stressing Over Delivery Dates:
  “You shouldn’t expect a baby to pay attention to what is, after all, a fairly arbitrary metric.”
  — Tim Harford (paraphrasing Prof. Gardosi), 08:38

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Timestamped Guide to Major Segments

• 00:19–03:35: The optimal stopping problem in dating; explanation and discussion of assumptions.
• 04:03–05:39: Listener question on pregnancy due dates and introductory banter.
• 05:39–06:01: Methods for estimating due dates in pregnancy.
• 06:01–07:03: The statistical likelihood of babies being born on their due dates.
• 07:20–08:27: Why doctors use due dates, and the real-world stats around timing.
• 08:27–08:38: Reassurance for expectant mothers about due dates.

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Conclusion

This episode of More or Less uses wit and expert insight to expose the strengths and limitations of applying mathematical models to life events, whether love or childbirth. Listeners come away with both practical guidance (“don’t sweat the due date!”) and a healthy skepticism of how tidy math formulas map onto messy human realities.

Transcript

[Narrator]

This is the short edition of More

[Tim Harford]

or Less first broadcast on the BBC World Service.

[BBC Announcer]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldservice.com podcasts

[Tim Harford]

hello and welcome to More or Less on the BBC World Service. I'm Tim Harford. This week, pregnancy due dates. But before that, we'll hear from Matt Parker. An unusual combination of mathematician and stand up comedian Matt recently wrote a book called Things to Make and do in the Fourth Dimension. It's a collection of tricks, games and puzzles that reveal bigger lessons about the world around us. Maths says Matt, can even help you find the right life partner. So I laid myself down on his couch and I opened my heart.

[Matt Parker]

I'm pleased to say I'm happily married, but occasionally I have doubts as to whether maybe I settled down too soon. Could I have done better if I waited? Seems unlikely, but it's quite possible my wife could have done better if she had waited. So can maths help me?

[Mathematician/Expert]

I mean, these are very valid concerns and ones you should probably not broadcast on radio. But there is a mathematical approach you could have taken and the problem you were faced, in fact we're all faced with, is when you're looking for a life partner, as you're interviewing people, or I believe dating is what it's commonly called. If you meet a candidate and you assess their qualities and then you reject them later on, it's very hard to go back and say, look, I've changed my mind. It turns out you were the best I'm ever going to do. But on the flip side, if you settle down with someone straight away, you have no idea what the general quality of possible candidates was. So you're faced with a problem. You've got to interview or survey a certain number of possible candidates and reject them to get a sense of the quality. But you don't want to do that for too many, or you may pass by the best option. And so the question is, how many people do you reject to get a sense of the standard? And at what point do you stop rejecting and you start choosing? And that is called the optimal stopping problem. And mathematically we know if you want to get the best person on average, you need to look at the total number of people you will date across your life. You then calculate the square root of that number of people. And so let's say you were going to date 100 people in your life. Your square root is 10. You then go through that first 10 people and you automatically reject them, but you keep track. I mean, maybe log them in a spreadsheet as to who was the best. And then once you've gone through that, you then keep dating people until you meet someone who is as good as or better than anyone you saw in your original sample as such. And that mathematically will give you the best result on average.

[Matt Parker]

There are all sorts of assumptions that we're making with the optimal stopping problem, not only the distribution of partners, but what counts as an interview or a date. How long do you need to date somebody before you can assess their quality? We're sort of assuming quality doesn't change, you don't change, your partner doesn't change. There's no role for divorce in this scenario. We're assuming that you know with certainty how many people you could possibly date over the course of your life. So there are all sorts of tweaks we could make and they might totally change the answer. And so, at the risk of being a killjoy, I have to say, well, what's the point of this if it's not going to give us an answer that really works in the real world? Why are we doing it at all?

[Mathematician/Expert]

You're absolutely correct. I mean, as always, a mathematical model is only as good as the starting assumptions, how many things you factor in and how accurate you are at factoring those in. And so I wouldn't recommend living life following this down to the algorithm to, you know, clinically locate the person you have then calculated to be your best partner. But it isn't a reasonably good guide. Research seems to show that people, on average, settle down too soon.

[Tim Harford]

Matt Parker. Now, when you found the one, it can lead to thoughts of babies. It certainly turned out that way for loyal listener Penelope Chaney, who's been in touch with a question.

[Narrator]

I'm expecting a baby in April and discovered that one of my close friends is also expecting a baby on the same day.

[Tim Harford]

That close friend is Eleanor Marshall, and the day in question is the 4th of April.

[Narrator]

This led us to wonder what the probability was of these two children actually having the same birthday and whether, you know, obviously whether they'd be born on their due dates or different days. But what the chances were of those children who have started in a similar way actually having the same birthday in the long term.

[Matt Parker]

Well, we don't know how similar a way they started. We.

[Tim Harford]

I don't think we need to go

[Narrator]

into that, but that's not what they meant.

[Matt Parker]

I imagine the details are broadly the same, but.

[Tim Harford]

So thank you, Penelope.

[Matt Parker]

So, Eleanor Your friend, you're on the line as well.

[Tim Harford]

Did Penelope tell you she was emailing us about this?

[Eleanor Marshall]

No, she didn't.

[Matt Parker]

Oh, how naughty.

[Eleanor Marshall]

But she told me once you had got in touch with her and expressed an interest in exploring this a little bit more. And to be honest, I'm quite intrigued myself to know what the odds are.

[Tim Harford]

Well, so were we. So let's start with the question of how the expected date of delivery is calculated. We got on to Jason Gardosi of the Perinatal Institute in the uk, who told us that this used to be done by adding 280 days to the date of a woman's last period. But in many places that's now regarded as rather old fashioned.

[Professor Jason Gardosi]

That is old school, although still being practiced in many areas in many countries and is really the first step whereby you use the first day of the last menstrual period from which to then count the length of pregnancy.

[Tim Harford]

Professor Gardozzi told me that studies had shown that dating through ultrasound by measuring the size of the fetus is actually a more accurate measure. Both Penelope and Eleanor's expected dates of delivery were calculated from their ultrasound scans. So that's a good start. Penelope already has one child and Eleanor has two. Both of their pregnancies this time around are straightforward and low risk. So given all this, how likely is it that women like them will deliver on the dates given to them?

[Professor Jason Gardosi]

Well, actually, most babies are not born on the predicted or estimated date of delivery, but in fact only about 4%.

[Tim Harford]

It's 4.4% to be precise. And that's for women who have a completely normal pregnancy. And that's using UK expected dates of delivery, because these things are done differently all around the world. So the chances of our two expectant mothers both delivering on the 4th of April really don't look good. They're about 1 in 500, in fact.

[Matt Parker]

So is that disappointing?

[Eleanor Marshall]

I don't think it makes a huge difference. It's not like, you know, it's a wonderful coincidence, but it's not like we did it on purpose, hoping that they would share a birthday.

[Matt Parker]

That would be weird.

[Eleanor Marshall]

It really would. We're not that close friends.

[Tim Harford]

So if the estimated date of delivery is wrong so often, why do we even need it? Professor Gardozzi says it's a useful metric not for patients, but for doctors. Medical professionals use it as a benchmark to let them evaluate test results and judge how the baby's developing. If we set aside premature births and other problem pregnancies and focus only on normal pregnancies the figures show that 94% of babies are born within two weeks of the estimated date of delivery. In the UK, they're actually marginally more likely to be born four days overdue than on the estimated date of delivery. Now, there's almost no chance that Penelope and Eleanor will both have their babies on the 4th of April. But what about the chance that whether early or late, two full term babies with the same estimated date of delivery are in fact born on the same date? Give me a break. It's not that interesting. It's one in 30.

[Professor Jason Gardosi]

Wow.

[Narrator]

That's quite high then.

[Eleanor Marshall]

That is quite high.

[Tim Harford]

There you go.

[Matt Parker]

Are you pleased?

[Narrator]

Well, it's higher than I thought it would be.

[Eleanor Marshall]

Yeah, definitely.

[Tim Harford]

So what should we take away from this then? Professor Gardosi doesn't like the term due date. It smacks too much of a deadline. His message for expectant mothers is that if your baby seems overdue, that's no reason to be anxious. You shouldn't expect a baby to pay attention to what is, after all, a. A fairly arbitrary metric. Thank you for listening. We love hearing from you too. You can email your comments and questions to us and our address is more or less BBC.co.uk and you can download this program and many previous editions at our website, BBC.com more or less.

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